Question

Find the mean deviation from mean and its coefficient for the given data:

X	0−10	10−20	20−30	30−40	40−50	50−60
F	3	5	7	2	9	4

Answer 1

Values (X)	Frequency (f)	Mid-Values (m)	fm	$\left|{\mathit{d}}_{\overline{X}}\right|\mathbf{=}\left|\mathit{m}\mathbf{-}\overline{\mathit{X}}\right|$	$\mathit{f}\mathbf{\times }\left|{\mathit{d}}_{\overline{\mathbf{X}}}\right|\mathbf{=}\mathit{f}\left|\mathit{d}\overline{{}_{\mathbf{X}}}\right|$
0−10	3	5	15	27	81
10−20	5	15	75	17	85
20−30	7	25	175	7	49
30−40	2	35	70	3	6
40−50	9	45	405	13	117
50−60	4	55	220	23	92
	Σf = 30		Σfm=960		Σ$f\left|d_{\overline{X}}\right|$=430

$$\begin{gathered} \mathrm{Mean},\overline{X}=\frac{\Sigma fm}{\Sigma f}=\frac{960}{30}=32 \\ \mathrm{Mean}\mathrm{deviation}\mathrm{from}\mathrm{Mean},\left(M.D_{\overline{X}}\right)=\frac{\Sigma f\left|d\overline{{}_X}\right|}{\Sigma f}=\frac{430}{30}=14.33 \\ \mathrm{Coefficient}\mathrm{of}\mathrm{M}.\mathrm{D}.=\frac{M.D_{\overline{X}}}{\overline{X}}=\frac{14.33}{32}=0.44 \end{gathered}$$